Algebra - Surds & Indices - Previous Year CAT/MBA Questions
The best way to prepare for Algebra - Surds & Indices is by going through the previous year Algebra - Surds & Indices OMET questions. Here we bring you all previous year Algebra - Surds & Indices OMET questions along with detailed solutions.
It would be best if you clear your concepts before you practice previous year Algebra - Surds & Indices OMET questions.
If is a whole number then which one of the statements below is consistent with it?
- (a)
a = 3, b = 2, c = 1
- (b)
a = 3, b = 1, c = 1
- (c)
a = 2, b = 1, c = 2
- (d)
a = 2, b = 1, c = 1
- (e)
a = 1, b = 2, c = 2
Answer: Option A
Explanation :
Let us prime factorize all the terms under the cube root sign.
7a × (35)(b+1) × (20)(c+2) = 7a × 5b+1 × 7b+1 × 22(c+2) × 5c+2
= 22(c+2) × 5b+c+3 × 7a+b+1
We have to calculate cube-root of this expression, hence powers of all prime numbers should be divisible by 3 for cube-root to be a whole number.
∴ 2(c + 2), (b + c + 3) and (a + b + 1) all should be multiples of 3.
Only option (a) satisfies this given condition.
Hence, option (a).
Workspace:
If x = 8 - and y = 2 + √2, then is given by:
- (a)
16x2/25
- (b)
64x2/81
- (c)
25y2/16
- (d)
81x2/64
Answer: Option D
Explanation :
x = 8 − √32 = 8 − 4√2 = 4(2 − √2)
=
On rationalising, we get
= = =
∴ x + 1/y = x + x/8 = 9x/8
⇒ = = =
Hence option (d).
Workspace:
The highest number amongst and
- (a)
- (b)
- (c)
- (d)
None of the above
Answer: Option B
Explanation :
Since the powers are (1/2), (1/3), (1/4), raise them to their LCM i.e. 12.
Hence, the terms become (26)1/12; (34)1/12 and (43)1/12 i.e. (64)1/12; (81)1/12 and (64)1/12
Since 81 > 64, the largest value would be ∛3.
Hence, option (b).
Workspace:
The value of x for which the equation will be satisfied is:
- (a)
1
- (b)
2
- (c)
3
- (d)
4
Answer: Option D
Explanation :
Substituting values given in options, the equation is satisfied for x = 4.
Hence, option (d).
Workspace:
The simplest value of the expression is:
- (a)
4
- (b)
8
- (c)
4p
- (d)
8p
Answer: Option B
Explanation :
Hence, option (b).
Workspace:
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